Which of the following numbers is a factor of 140? ${3,6,8,10,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $140$ by each of our answer choices. $140 \div 3 = 46\text{ R }2$ $140 \div 6 = 23\text{ R }2$ $140 \div 8 = 17\text{ R }4$ $140 \div 10 = 14$ $140 \div 13 = 10\text{ R }10$ The only answer choice that divides into $140$ with no remainder is $10$ $ 14$ $10$ $140$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $140$ $140 = 2\times2\times5\times7 10 = 2\times5$ Therefore the only factor of $140$ out of our choices is $10$. We can say that $140$ is divisible by $10$.